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lfunc_lfunctions • Show schema
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{'Lhash': '1179460849815774510788790573336', 'a10': [-9169.27878157571, -23362.941313727413], 'a2': [-8.685242960336174, 8.058727778419536], 'a3': [-21.806404204216246, 3.2867865903384548], 'a4': [-27.771456042850854, 370.5843267431965], 'a5': [-773.9054629628251, 1971.8789606336318], 'a6': [162.90660020761695, -204.27841540382644], 'a7': [-2448.0243844604256, -5861.8071968538125], 'a8': [-6527.454565061288, -8185.169130482211], 'a9': [-18343.823238061377, 5658.320104085991], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 25.23675597202979, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [2448.0243844604256, 5861.8071968538125]]]], 'bad_primes': [7], 'central_character': '49.11', 'coefficient_field': 'CDF', 'conductor': 49, 'conductor_radical': 7, 'conjugate': '41958367532430679093485457812', 'degree': 2, 'euler_factors': [[[1.0, 0], [8.685242960336174, -8.058727778419536], [38.26180791624922, -510.5683441567642]], 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'root_number': '0.572502143093229 + 0.8199032236512185*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.15298640900720897', 'prec': 64}, 'spectral_label': 'c9-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.930430553658415735687013561141593', 'prec': 117}, 'z2': {'__RealLiteral__': 0, 'data': '2.81863940408267374739092764160533', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '5.10034137461088733459108620156037', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 25.23675597202979, 'bad_primes': [7], 'central_character': '49.11', 'conductor': 49, 'conductor_radical': 7, 'degree': 2, 'index': 23, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/49/10/g/a/11/16'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-7e2-49.11-c9-0-23', 'motivic_weight': 9, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [9], 'order_of_vanishing': 0, 'prelabel': '2-7e2-49.11-c9-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.023619807671535, 'root_angle': 0.15298640900720897, 'self_dual': False, 'spectral_label': 'c9-0', 'z1': {'__RealLiteral__': 0, 'data': '0.930430553658415735687013561141593', 'prec': 117}}
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lfunc_instances • Show schema
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{'Lhash': '1179460849815774510788790573336', 'Lhash_array': ['1179460849815774510788790573336'], 'factors': ['2-7e2-49.11-c9-0-23'], 'label': '2-7e2-49.11-c9-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/49/10/g/a/11/16'}